These Parquet files were created by modifying Impala's HdfsParquetTableWriter.

String Data
-----------
These files have a single nullable string column 's'.

dict-encoded-negative-len.parq: a single dictionary-encoded value with a negative length.
dict-encoded-out-of-bounds.parq: a single dictionary-encoded value with a length past end of page.
plain-encoded-negative-len.parq: a single plain-encoded value with a negative length.
plain-encoded-out-of-bounds.parq: a single plain-encoded value with a length past end of page.

Decimal Data
-----------
illegal_decimals.parq has 8 decimal columns(d1, d2, ..., d8). All of them have illegal schema in the footer.
Generated by modifying HdfsParquetTableWriter::WriteFileFooter by these:

 Status HdfsParquetTableWriter::WriteFileFooter() {
+  file_metadata_.schema[1].__set_precision(0);
+  file_metadata_.schema[1].__isset.precision = false;
+  file_metadata_.schema[1].logicalType.DECIMAL.precision = 0;
+  file_metadata_.schema[1].logicalType.__isset.DECIMAL = false;
+
+  file_metadata_.schema[2].__set_precision(20);
+  file_metadata_.schema[2].logicalType.DECIMAL.precision = 20;
+  file_metadata_.schema[2].logicalType.__isset.DECIMAL = true;
+  file_metadata_.schema[2].__isset.logicalType = true;
+
+  file_metadata_.schema[3].__set_precision(-1);
+  file_metadata_.schema[3].logicalType.DECIMAL.precision = -1;
+  file_metadata_.schema[3].logicalType.__isset.DECIMAL = true;
+  file_metadata_.schema[3].__isset.logicalType = true;
+
+  file_metadata_.schema[4].__set_type(parquet::Type::FIXED_LEN_BYTE_ARRAY);
+  file_metadata_.schema[4].__isset.type_length = false;
+
+  file_metadata_.schema[5].__set_type(parquet::Type::FIXED_LEN_BYTE_ARRAY);
+  file_metadata_.schema[5].__set_type_length(0);
+
+  file_metadata_.schema[6].__set_scale(-1);
+  file_metadata_.schema[6].logicalType.DECIMAL.scale = -1;
+  file_metadata_.schema[6].logicalType.__isset.DECIMAL = true;
+  file_metadata_.schema[6].__isset.logicalType = true;
+
+  file_metadata_.schema[7].__set_scale(4);
+  file_metadata_.schema[7].__set_precision(2);
+  file_metadata_.schema[7].logicalType.DECIMAL.scale = 4;
+  file_metadata_.schema[7].logicalType.DECIMAL.precision = 2;
+  file_metadata_.schema[7].logicalType.__isset.DECIMAL = true;
+  file_metadata_.schema[7].__isset.logicalType = true;

Then create the table and insert one row into it:

create table my_decimal_tbl (d1 decimal(4,2), d2 decimal(4,2), ..., d7 decimal(4,2)) stored as parquet;
insert into my_decimal_tbl values (cast(0 as decimal(4,2)), cast(0 as decimal(4,2)), ...);